Abstract
A gauge theory of GL(2) gauge group is considered on a complex manifold and hermitian connections of holomorphic vector bundles of rank 2 over a compact complex manifold M are abelianized using monoidal transformation. The abelianized connections of the line bundle over a manifold M̃ as a P 1 fibre over M are constructed explicitly. The Wilson loop of the GL(2, C) gauge theory is abelianized to that of C ∗ gauge theory. By this the Polyakov conjecture is verified for a GL(2) gauge theory on a complex manifold.
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